Hello everyone. Now, I don't know if this belongs here (there may be some advanced theorem) or it belongs in the pre-university forum. Mods, feel free (as though I'd have a say) to move this.

This may be a very stupid question, but basic probability has never been my forte. Is there a mathematical principle which models the following

You flip a coin and tally the values "heads" and "tails" in two columns, call them A and B. At a given flip

define

. It seems to make sense that

will alternate signs infinitely often.

What is this called?